Remarkably, systematic bounds can be placed on possible corrections
to Einstein gravity [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. Such
corrections naturally appear due to the presence of heavy particles in
the theory. To leading order in Newton's constant \(G\) , such particles
can be exchanged at tree-level, as in string theory, or at one-loop,
as in the case of matter minimally coupled to gravity. By expanding
such amplitudes at low energies and matching to a low-energy effective
field theory one finds an infinite series of higher-derivative
corrections to Einstein gravity. The coefficients in front of these
higher-derivative operators, or Wilson coefficients, satisfy various
bounds due to unitarity and causality of the underlying
amplitude [1]}, [2]}. In this paper, we focus on
the leading corrections to Einstein
gravity.In particular, higher-loop effects
do not affect the discussion in this paper since by assumption
gravity is weakly coupled and we are focusing on the leading-order
effect. A central question, which we investigate in this paper, is
to understand if there are principles that can greatly
restrict the values of physically allowed Wilson coefficients.
